Quantum Stochastic Resonance
Comunicación # ... #... # Información Relevante #Over the last two decades, stochastic resonance has continuously attracted considerable attention. The term is given to a phenomenon that is manifest in nonlinear systems whereby generally feeble input information (such as a weak signal) can be be amplified and optimized by the assistance of noise. The effect requires three basic ingredients: (i) an energetic activation barrier or, more generally, a form of threshold; (ii) a weak coherent input (such as a periodic signal); (iii) a source of noise that is inherent in the system, or that adds to the coherent input. Given these features, the response of the system undergoes resonance-like behavior as a function of the noise level; hence the name stochastic resonance. C6 #Because quantum noise persists even at absolute zero temperature, the transport of quantum information should naturally be aided by quantum fluctuations as well. Indeed, quantum mechanics provides the nonlinear system with an additional channel to overcome a threshold. This additional channel is provided by quantum tunneling, i.e., a particle can tunnel through a barrier without ever going over it. As a matter of fact, we shall see that the classical stochastic resonance effect can be assisted by quantum tunneling contributions even at finite temperatures. For strongly damped systems, such contributions can enhance the classical stochastic resonance effect up to two orders of magnitude. C6 #Let us first focus on the regime T*T0 , where quantum tunneling is not the dominant escape path, but nevertheless leads to significant quantum corrections. C6 #The situation changes drastically when we proceed towards the extreme cold. Here, we shall focus on the deep quantum regime, where tunneling is the only channel for barrier crossing. In this low-temperature regime, periodic driving induces several new interesting, counterintuitive physical phenomena, such as ‘‘coherent destruction of tunneling’’ (Grossmann et al., 1991), the ‘‘stabilization of dissipative coherence’’ with increasing temperature (Dittrich et al., 1993; Oelschla¨gel et al., 1993), or the effect of driving-induced quantum coherence (Grifoni et al., 1995). C6 #We predict theoretically the enhancement of quantum coherence in a superconducting flux qubit by a classical external noise. First, the off-diagonal components of the qubit density matrix are increased. Second, in the presence of both ac drive and noise, the resulting Rabi oscillations survive “in perpetuity”, i.e. for times greatly exceeding the Rabi decay time in a noiseless system. The coherence-enhancing effects of the classical noise can be considered as a manifestation of quantum stochastic resonance and are relevant to experimental techniques, such as Rabi spectroscopy. C7 #In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir who predicted them in 1948. The typical example is of the two uncharged conductive plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them.1 When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force2—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization.F1 Relaciones *... *... *... Fuentes F1 https://en.wikipedia.org/wiki/Casimir_effect F2 ... F3 ... Fuentes Científicas C1 Nonlinear quantum stochastic resonance http://www.physik.uni-augsburg.de/theo1/hanggi/Papers/182.pdf (copy http://ge.tt/7apXxcf2) C2 http://www.scholarpedia.org/article/Stochastic_resonance C3 This simulation illustrates the phenomenon of stochastic resonance. An overdamped particle in a periodically oscillating double-well potential is subjected to Gaussian white noise, which induces transitions between the potential wells. https://www.youtube.com/watch?v=HbJ_I3xbIMg C4 This numerical simulation shows the behavior of a particle in a double-well potential with a weak periodic input. Here transitions are assisted by noise. https://www.youtube.com/watch?v=DvN4Nv4Am6s C5 Uploaded on Feb 13, 2009 This is a Quantum Tunneling simulation in Mathematica that solves the time-dependent schroedinger equation. Here, a gaussian wavepacket is placed in a potential system that has two stable states (bistable). This simulation was created as a quantum extension of the classic stochastic resonance phenomenon, where a particle oscillates between the two stable states. Here, however, the probability density function (pdf) of the particle's postion is not a delta function (and thus could have a finite density in both wells simultaneously). However, in this case, the pdf seems to pass through a half-period of oscillation between two wells, and it is possible that a longer simulation will reveal the clear oscillation. However, this is still not a recreation of stochastic resonance - which needs a periodic and a random fluctuation of the potential. This work is currently in progress. This plot shows the progression of the probability density of the single-dimensional wavepacket in time. Created by Biswaroop Mukherjee under the guidance of Dr. Antonio Nassar as a part of a Studies in Scientific Research project in Harvard-Westlake School, North Hollywood, CA. https://www.youtube.com/watch?v=SKatmNFzmis C6 Stochastic resonance http://www.physik.uni-augsburg.de/theo1/hanggi/Papers/195.pdf C7 Noise-induced quantum coherence and persistent Rabi oscillations in a Josephson flux qubit. https://arxiv.org/pdf/0904.2686.pdf